It must be tough when they've long fled the nest or live far away. I listen, show I care, we problem solve together, and I give advice when asked. I share my perspective, and I validate their feelings and let them know I'm always here. My kids come to me and talk about everything. I often do things to let them know they're valued.
From the other perspective, my mother actively disliked me and made sure I felt it, "I love you because you're my child, but I don't like you" is a strong memory for me! I self-harmed and had depression as a teen. She made it all about herself and never once tried to understand me or what I needed. She talked to everyone else though, even strangers, about how she was 'so upset and worried for her daughter'. The lack of trust or bond was the biggest problem for me, so I've prioritised having that in my own family. My own parents didn't share much, so adulthood hit me hard with it's unexpected difficulties. I've been open from an appropriate age, that adults have problems too and we work it out, so they knew they might face hard things and will get through it too.
I was in an abusive relationship in my 20s, and when the police got involved, my mum told everyone how upset SHE was, without ever knowing what I went through or trying to support me. In my 30s and increasingly disabled, she moved to my village and meets up with acquaintances, telling them how worried she is. In reality, she's nasty and never helps with anything. I feel violated that she talks about (her perception of) me to strangers. I also have a childless relative who regularly tells people she's worried about me, but has met me a dozen times my whole life!
So, I see both sides when someone says they're worried for their children. I wonder if they really know why their child is struggling, of if they nurtured them so they had a strong base to grow resilience and coping skills. When someone says they're worried for their adult kids, I wonder why they don't talk to those kids about it. I wonder if they even know what those kids need, or if they're telling others instead of doing it. Sometimes the mum is worried about something far from the reality of the adult-childs actual experience, simply because they catastrophize or are lonely themselves. Sometimes it's because they're critical and are worried because of judgemental expectations!
I think it comes down to being close with your kids and ensuring they know you're always there for them. If they need help, they'll be comfortable to ask. Get therapy for yourself to reframe things, so they don't feel a burden or worried they can't share. Call them, meet up, send them something thoughtful, pamper them, cry with them, show your pride, remind them of their value, just listen. I had a friend whose dad moved in and did all the housework when she got divorced, I thought that was lovely! Another, her mum travelled to her every month to have a movie night and make her breakfast in bed, then took the grandkids out for the afternoon so she could rest. She was still doing it 2 years post divorce!
You know you've done everything you can, life can't be perfect, but they have the capacity to get through it just as you have.